Washington -LRB- CNN -RRB- -- Mitt Romney on Tuesday did n't back away from remarks he made in a secretly recorded video casting supporters of President Barack Obama as dependent on welfare , and instead said the comments that generated more problems for him in a tight race were an honest reflection of his campaign 's message .

`` This is a message I 'm carrying day and day out and will carry over the coming months , '' Romney said on Fox News . `` This is a decision about the course of America , where we 're going to head . We 've seen the president 's policies play out over the last four years . ''

Romney cited an opposition research video that Republicans began circulating on Tuesday afternoon that shows Obama speaking at Loyola University in 1998 about making government more effective .

`` I think the trick is how do we structure government systems that pool resources and hence facilitate some redistribution , because I actually believe in redistribution , at least at a certain level , to make sure that everybody 's got a shot , '' Obama is heard saying .

` Anatomy of a leak ' of the Mitt Romney video

In his interview Tuesday , Romney framed Obama 's remarks as an endorsement of redistributing private wealth , rather than on making sure government agencies were well supported .

`` The president 's view is one of larger government , '' Romney said . `` There 's a tape that came out today where the president 's saying he likes redistribution . I disagree . I think a society based upon a government centered nation where government plays a larger and larger role , redistributes money , that 's the wrong course for America , that will not build a stronger America , or help people out of poverty . ''

Republicans have used the issue against Obama in the past .

Romney 's charged comments at a May fund-raising event were recorded with a hidden camera . The video shows him telling his donors that nearly half of Americans back Obama because they rely on government support .

`` There are 47 percent of the people who will vote for the president no matter what , '' Romney says in one clip first posted on Monday afternoon . `` There are 47 percent who are with him , who are dependent on government , who believe that , that they are victims , who believe that government has the responsibility to care for them . Who believe that they are entitled to health care , to food , to housing . ''

The fund-raiser video was the latest in what has been a shaky stretch for the Romney campaign following last month 's political conventions and as the candidates hurtle toward three presidential debates next month .

How candidates are preparing for the debates

Romney 's remarks generated reaction from both sides of the political spectrum .

The president suggested that Romney was `` writing off a big chunk of the country . ''

In an interview taped for the `` Late Show with David Letterman '' in New York , Obama said he did n't know what Romney was referring to in the video but was quick to add , `` One of the things I learned as president is you represent the entire country . If you want to be president , you have to work for everyone . ''

Obama was caught in a secret camera moment in 2008 , when he was recorded at a private fund-raiser saying that some voters `` cling to their guns and religion . '' At the time , Republicans quickly pounced on the comment and now Romney 's running mate , Congressman Paul Ryan , uses the quote against the president on the campaign trail .

Conservative commentator William Kristol wrote in his Weekly Standard column Tuesday that Romney 's comments insulted some of his own supporters -- such as senior citizens on Medicare .

However , other conservatives supported Romney for highlighting what they call the increasing dependency of American society on government programs .

The latest flap also bled into other races , including two contests viewed as crucial for Republican hopes of taking control of the Senate .

Sen. Scott Brown of Massachusetts and challenger Linda McMahon in Connecticut sought to distance themselves from Romney 's remarks .

`` As someone who grew up in tough circumstances , I know that being on public assistance is not a spot that anyone wants to be in . Too many people today who want to work are being forced into public assistance for lack of jobs , '' Brown said .

CNN Fact Check : Who really receives government assistance ?

But it was n't an entire lost day for Romney .

The latest Gallup daily tracking poll showed the post-convention bounce for Obama fading .

The survey 's seven-day rolling average shows 47 % of registered voters supporting Obama and 46 % supporting Romney , returning the race to narrow , pre-convention margins .

A CNN poll taken the week after the Democratic National Convention earlier this month showed Obama with a six point advantage .

Democrats pounce on Romney comments

A CNN-ORC poll conducted after the Democratic convention showed Obama with a 52 % -46 % lead over Romney after the two were tied at 48 % in the same poll the previous week . And a Washington Post poll released Tuesday showed Obama continuing to lead Romney in Virginia , one of the vital battleground states of 2012 .

CNN 's Polling Center

Another clip from the event , posted later Monday , shows Romney questioning the prospect of ever reaching peace between Israelis and Palestinians .

`` I 'm torn by two perspectives in this regard , '' Romney is shown saying . `` One is the one which I 've had for some time , which is that the Palestinians have no interest whatsoever in establishing peace , and that the pathway to peace is almost unthinkable to accomplish . ''

Romney goes on to describe the obstacles he sees toward developing a so-called `` two-state solution '' that would establish an independent Palestinian state alongside Israel . He cites problems of geography , including the proximity to Tel Aviv of a potential border between the two states , as preventing any real progression toward the two states .

`` These are problems - these are very hard to solve , all right ? '' Romney says on the tape . `` And I look at the Palestinians not wanting to see peace anyway , for political purposes , committed to the destruction and elimination of Israel , and these thorny issues , and I say , ` There 's just no way . ' ''

In public , Romney has previously declared support for the two-state solution .

CNNMoney 's Jeanne Sahadi and CNN 's Tom Cohen , Ashley Killough , Jim Acosta , Kevin Liptak and Rachel Streitfeld contributed to this report .

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NEW : Romney not backing away from controversial comments

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NEW : Obama says in interview that the president represents entire country

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NEW : Republicans in key Senate races seek to distance themselves from Romney comments

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NEW : Tracking poll shows Obama bounce fading overall ; Other poll shows Obama still leads in Virginia